1. Modeling with Linear Equations MATH 102 Contemporary Math S. Rook

2. Overview Section 7.2 in the textbook: – Building equations with a point and a slope – Building equations using two points

3. Building Equations with a Point and a Slope

4. Recall the slope-intercept form of a line y = mx + b What is the significance of m & b? Recall that points are comprised of two parts: – The x-part and y-part Given the slope m and a point, we can solve for b Finally, we obtain an equation by filling in the values for m & b and keeping x & y as variables – e.g. Find the equation of a line with a slope of 1 and passes through (3, 2)

5. Building Equations with a Point and a Slope (Example) Ex 1: Find a linear equation with the given point and slope: a) Slope 4; Point (-2, 6) b) Slope -8; Point (-4, -9)

6. Building Equations Using Two Points

7. 7 If we are given only two points, what element are we missing? How do we calculate the slope between two points? We now have a choice of which point to use in the slope-intercept formula – It does not matter which point is used – the same equation will result

8. Building Equations Using Two Points (Example) Ex 2: Find a linear equation that passes through the given points: a) (17, 12) and (9, 10) b) (11, -4) and (-8, 2)

9. Building Equations Using Two Points (Example) Ex 3: According to the Consumer Electronics Association, the number of direct satellite dish receivers rose from 4.3 million in 2000 to 16.8 million in 2004. a) Construct a linear equation relating the year to the number of satellite dishes b) In which year will there be 40 million receivers?

10. Summary After studying these slides, you should know how to do the following: – Write a linear equation given the slope and a point – Write a linear equation given two points Additional Practice: – See problems for Section 7.2 Next Lesson: – Systems of Linear Equations (Section 8.1)